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Math Help - geometry in complex numbers

  1. #1
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    geometry in complex numbers

    Represent the following region in the complex plane by equations or inequalities in the variable
    z.

    All the points outside a circle of radius 3, centered at x=-1, y=-2.

    i drew the circle -4< x < 2 and -5<y<1

    so how do we do the equation or the inequality?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by sandy View Post
    Represent the following region in the complex plane by equations or inequalities in the variable
    z.

    All the points outside a circle of radius 3, centered at x=-1, y=-2.

    i drew the circle -4< x < 2 and -5<y<1

    so how do we do the equation or the inequality?
    A circle of radius R around a complex number z_0\in\mathbb{C} is defined to be \left\{z\in\mathbb{C}:|z-z_0|=R\right\}
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    A circle of radius R around a complex number z_0\in\mathbb{C} is defined to be \left\{z\in\mathbb{C}:|z-z_0|=R\right\}
    i didnt understand, the equation of a circle is |z-z_0|=R but how do we do the above as an inequality or equation?
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    \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}.
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  5. #5
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    Quote Originally Posted by Plato View Post
    \left\{ {z:\left| {z - \left( { - 1 - 2i} \right)} \right| > 3} \right\}.
    oh ok thankyou very much now i understood what they want and how to solve questions like that. thanks again
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